Solve for $x$ : $4\sqrt{x} + 1 = 2\sqrt{x} + 8$
Solution: Subtract $2\sqrt{x}$ from both sides: $(4\sqrt{x} + 1) - 2\sqrt{x} = (2\sqrt{x} + 8) - 2\sqrt{x}$ $2\sqrt{x} + 1 = 8$ Subtract $1$ from both sides: $(2\sqrt{x} + 1) - 1 = 8 - 1$ $2\sqrt{x} = 7$ Divide both sides by $2$ $\frac{2\sqrt{x}}{2} = \frac{7}{2}$ Simplify. $\sqrt{x} = \dfrac{7}{2}$ Square both sides. $\sqrt{x} \cdot \sqrt{x} = \dfrac{7}{2} \cdot \dfrac{7}{2}$ $x = \dfrac{49}{4}$